I'm not getting an acceptable answer when I use Wolfram to solve the systems produced. I believe the error is that I need to combine the impedances of the capacitor and the inductor coming off of node 2, but I'm not sure since there is another node there. It's quite possible there are multiple errors on my part.

Staff: Mentor

There is no restriction on what impedance can comprise each branch; it doesn't have to be a single element. In your eqn (2) you need to replace 1/(j3E4) by 1/(z) where z is the series impedance of the capacitor and inductor.

So there's a little sub-exercise for you, determining that series impedance before using it in eqn (2).